Question: If $a \text{ Y } b$ is defined as $a \text{ Y } b = a^2 - 2ab + b^2$, what is the value of $3 \text{ Y } 2$?
We have $3 \text{ Y } 2 = 3^2-2(2)(3)+2^2 = 9+4-12 = \boxed{1}$.

Alternatively, you could notice that $a^2-2ab+b^2=(a-b)^2$, so the answer is simply $(3-2)^2 = 1^2 = \boxed{1}$.